Orientational deconvolution of two-dimensional static disorder by a Tikhonov regularized method for 2H solid state NMR of nano-tubular-oriented structures

Residual orientational disorder of deuterated nonadecane in hydrogenated urea nanotubes: single crystal 2H NMR

“…The method presented in this paper is a generalization to two-dimensional disorders in tubular structures which depend on azimuthal angle. Indeed, we showed recently [19] that a set of experimental spectra S e (m, b s ) acquired at different static magnetic field orientations b s , combined with an inverse method using Tikhonov regularization and positivity constraint leads to the orientationnal probability density of the C-D with a good reliability. Both approaches use a priori knowledge on the symmetry of the orientation distribution (axially symmetric or twodimensional disorder).…”

“…This general problem is under consideration. In this article, the twodimensional approach developed in [19] is adapted to the system under current interest.…”

“…We recently showed that these methods lead the orientational probability density of a rotationally disordered systems around a known axis from a set of single crystal 1D-spectra at different magnetic field orientations [19]. Therefore, once a reference axis of the mean host structure is known, the distribution of the alkane orientations with respect to this reference axis can in principle be reconstructed by performing single crystal NMR at different orientations.…”